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Manuel wants to buy a window shade to cover the window and frame shown. the window is in the shape of a regular octagon. the radius of the window, including the frame, is 2 ft, and the measure of each edge of the octagonal frame is 1.52 ft. what is the approximate area of the window that needs to be covered, including the frame?

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The area of the window may be determined through the equation,
                                         A = 0.5 aP
where A is area, a is apothem, and P is the perimeter. 

Given that the side measures 1.52 ft each, the perimeter of the octagon is 12.16 ft. The apothem is calculated by the equation,
                                             a = (cos 360/(8x2))(2 ft) = 1.8477 ft
Thus, the area of the octagon is,
                                      A = 0.5(1.8477 ft)(12.16 ft)
                                         A = 11.23 ft²
Tundexi

The approximated area of the window that will needs to be covered will be 11.23 ft².

How is area of the window determined?

Through this equation, the area of the window will be determined with the formula "A = 0.5 aP"where A is area, a is apothem, and P is the perimeter.

Given data

Side measures 1.52 ft each

Perimeter of the octagon is 12.16 ft.

Apothem a = (cos 360/(8x2))(2 ft) = 1.8477 ft

Estimated area of the octagon A = 0.5(1.8477 ft)(12.16 ft)

Estimated area of the octagon A  = 11.23 ft²

Therefore, the approximated area of the window that will needs to be covered will be 11.23 ft².

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